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    Re: Timing noon.
    From: Walter Guinon
    Date: 2002 Apr 10, 17:12 -0700

    A general method of estimating the clock time of local noon:
    
    1) Construct a time ordered series of the pair A = (ho,t) where ho is observed
    altitude and t is the attendant clock time.
    
    2)  Let T be the uncertainty in the time of local noon. For each value of
    |tau| < T in increments of  say 0.1 seconds,
    a) Compute the series B = [hc,(t+tau)] where hc is the computed altitude using
    the DR position and declination at time t+tau.
    b) For each value of tau compute C = the sum of the term by term products of ho
    and hc.
    
    3)   The value of t+tau associated with the largest C is the estimate of noon.
    
    In other words for each candidate tau we compute the series B, the variation of
    hc with time, then correlate this with the sequence of altitude measurements
    and proclaim noon based on tau that gives  the peak correlation.
    
    George Huxtable asks, "Should the navigator spend the whole day measuring, or
    are there times that
    are more useful than others?"
    Of course the more measurements the merrier, but certain times will contribute
    more to the accuracy of the solution than others. The measurements with the
    highest geometric strength are those with highest sensitivity to tau (i.e.
    measurements with largest d ho/d tau). Refraction aside, this means that the
    best measurements are those made shortly after sunrise and just before sunset.
    
    George asks "As I see it, no other input is required than altitudes of the Sun
    measured
    at suitably chosen times, a knowledge of the North-South component of the
    ship's speed, and the rate of change of declination. Does Walter agree?"
    
    I think the E/W component of the ship's speed must also be incorporated in the
    solution.
    
    --- George Huxtable  wrote:
    > Walter Guinon said-
    >
    > >When declination and Latitude are changing appreciably perhaps the most
    > general
    > >method of estimating the time of local noon is:
    > >1) Take altitude measurements of the sun when you can, hopefully between
    > >sunrise and sunset.
    > >2) The clock time of noon is that which gives a least mean squares fit of
    > this
    > >altitude/time data to the computed altitude at the DR position.
    >
    > George Huxtable responds-
    >
    > This, to me, is a bit too general to be really helpful. I wonder if Walter
    > Guinon could be a bit more specific, please, about points 1 and 2.
    >
    > Should the navigator spend the whole day measuring, or are there times that
    > are more useful than others?
    >
    > What is the "DR position" that he refers to, and what measurements has it
    > been derived from? Having chosen that position, how does he make the
    > least-squares fit?
    >
    > As I see it, no other input is required than altitudes of the Sun measured
    > at suitably chosen times, a knowledge of the North-South component of the
    > ship's speed, and the rate of change of declination. Does Walter agree?
    >
    > ------------------------------
    >
    > george---.u-net.com
    > George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > Tel. 01865 820222 or (int.) +44 1865 820222.
    > ------------------------------
    
    
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